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Statistics > Machine Learning

Title:Information Recovery in Shuffled Graphs via Graph Matching

Abstract: In a number of methodologies for joint inference across graphs, it is assumed
that an explicit vertex correspondence is a priori known across the vertex sets
of the graphs. While this assumption is often reasonable, in practice these
correspondences may be unobserved and/or errorfully observed, and graph
matching---aligning a pair of graphs to minimize their edge disagreements---is
used to align the graphs before performing subsequent inference. Herein, we
explore the duality between the loss of mutual information due to an errorfully
observed vertex correspondence and the ability of graph matching algorithms to
recover the true correspondence across graphs. We then demonstrate the
practical effect that graph shuffling---and matching---can have on subsequent
inference, with examples from two sample graph hypothesis testing and joint
graph clustering.